An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 69
lyconsider their more elementary properties, reserving for a laterchapter the complete discussion of them. Concurrent lines drawn through the verticesof a triangle. 94. If the straight lines which connect the vertices A, B,G ofa triangle with any point 0 7neet the opposite sides of the trianglein… … B X C By similar triangles, BX:XC = AM:]!fA,CY -.YA^BC : AM,AZ: ZB = NA : BG. Hence we have, BX CY AZ_,XCYAZB~ 95. If X,Y, Z are points on the sides of a triangle such that BX CY AZ_-.XC ■ YA ■ ZB~ the lines AX, BY, CZ will be concurrent. For let BY, CZ meet in the point 0, and let AO meet BG inX.…
Geometry
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